Logan Forsythe's double to left scored Bellinger, cutting the deficit to 4-3.
Darvish had allowed eight hits and three runs in the game, all on home runs.
Elvis Andrus had the go-ahead home run among his four RBIs, Cole Hamels won again despite a shaky outing and the Texas Rangers completed a three-game sweep of the Detroit Tigers with a 12-6 victory.
The last time a Dodgers team was this many games over.500 was in 1953, when four future Hall of Famers - catcher Roy Campanella, shortstop Pee Wee Reese, left fielder Jackie Robinson and center fielder Duke Snider - were playing for the Brooklyn Dodgers. He next is scheduled to throw a three-inning simulated game in five days or go on a rehab assignment.
After taking the first two matchups in the Bronx this week, the Yankees kept up their winning ways when the crosstown rivalry shifted to Queens. Ross Stripling (2-4) earned the win for pitching a flawless ninth. Baez opened the bottom of the ninth with a double off Wandy Peralta and pinch-hitter Jon Jay walked.More news: Tom Cruise Gets Severely Injured On Mission Impossible 6 Sets
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Darvish would go on to record his only two strikeouts of the game, to end the inning, but still finished with the lowest strikeout total of his career.
The Dodgers are 49-9 since June 7 and turned in another stellar performance Tuesday as Alex Wood tossed seven strong innings and rookie star Cody Bellinger reached base three times.
Leury Garcia got the long ball parade started when he hit a first-pitch fastball from Darvish just inside the right-field foul pole for a leadoff home run.
All four runs for the White Sox came via the solo home run.
The honorary member of the Dodgers "Slug Club", Kiké Hernandez, hit his 11 home run of the season when he tied the game off Rodon in the bottom half of the fourth inning.
The Minnesota Twins have postponed their game against the Cleveland Indians because of rain, scheduling a split doubleheader to finish the series.